Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections section A and section B of grade X. There are 32 students in section A and 36 students in section B.
If p and q are positive integers such that p = ab^{2} and q = a^{2}b, where a, b are prime numbers, then the LCM (p, q) is
Given, p = ab^{2} = a × b × b
q = a^{2}b = a × a × b
LCM of (p, q) = a^{2}b^{2}
Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections section A and section B of grade X. There are 32 students in section A and 36 students in section B.
If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is
Prime factor 32 is 2 x 2 x 2 x 2 x 2
Prime factor 36 is 2 x 2 x 3 x 3
HCF is 2 x 2 i.e 4
HCF of 32 and 36 is 4.
Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections section A and section B of grade X. There are 32 students in section A and 36 students in section B.
7 × 11 × 13 × 15 + 15 is a
Take 15 common
15 ( 7 × 11 × 13 + 1)
So, given number has factor other than 1 and itself so it is a composite number.
Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections section A and section B of grade X. There are 32 students in section A and 36 students in section B.
What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?
LCM(32, 36) = 2^{5} × 9 = 288
Hence, the minimum number of books required to distribute equally among students of section A and section B are 288.
Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections section A and section B of grade X. There are 32 students in section A and 36 students in section B.
36 can be expressed as a product of its primes as
36 = 2 × 2 × 3 × 3
= 2^{2} × 3^{3}
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
Find the sum of exponents of the prime factors of total number of plants.
The prime factors of 360 = 2 × 2 × 2 × 3 × 3 × 5
= 23 × 32 × 51
∴ Sum of exponents = 3 + 2 + 1 = 6.
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
Find the total number of plants
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
What is total numbers of row in which they can be planted
Number of rows of marigold plants = 225/45 = 5
Total number of rows = 3 + 5 = 8
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
What is the maximum number of columns in which they can be planted ?
No. of marigold plants = 225
The maximum number of columns in which they can be planted
= HCF of 135 and 225
∴ Prime factors of 135 = 3 × 3 × 3 × 5
and 225 = 3 × 3 × 5 × 5
∴ Prime factors of 135 = 3 × 3 × 5 = 45.
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
Find the sum of exponents of the prime factors of the maximum number of columns in which they can be planted.
So, prime factors of 45
= 3 × 3 × 5 = 3^{2} × 5^{1}
∴ Sum of exponents = 2 + 1 = 3.
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